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            <h1 id="seo-header">『计算机组成原理』数据的表示及其运算和运算器（附考研题目）</h1>
            
            
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                <h1 id="『计算机组成原理』数据的表示及其运算和运算器（附考研题目）"><a href="#『计算机组成原理』数据的表示及其运算和运算器（附考研题目）" class="headerlink" title="『计算机组成原理』数据的表示及其运算和运算器（附考研题目）"></a>『计算机组成原理』数据的表示及其运算和运算器（附考研题目）</h1><h3 id="数据的表示和运算"><a href="#数据的表示和运算" class="headerlink" title="数据的表示和运算"></a>数据的表示和运算</h3><h4 id="1-数制与编码"><a href="#1-数制与编码" class="headerlink" title="1.数制与编码"></a>1.数制与编码</h4><h5 id="（1）进位计数制及其相互转换（前期知识）"><a href="#（1）进位计数制及其相互转换（前期知识）" class="headerlink" title="（1）进位计数制及其相互转换（前期知识）"></a>（1）进位计数制及其相互转换（前期知识）</h5><h5 id="（2）真值和机器数（6-1）"><a href="#（2）真值和机器数（6-1）" class="headerlink" title="（2）真值和机器数（6.1）"></a>（2）真值和机器数（6.1）</h5><h5 id="（3）BCD-码（附录-5B）"><a href="#（3）BCD-码（附录-5B）" class="headerlink" title="（3）BCD 码（附录 5B）"></a>（3）BCD 码（附录 5B）</h5><h5 id="（4）字符与字符串（附录-5A）"><a href="#（4）字符与字符串（附录-5A）" class="headerlink" title="（4）字符与字符串（附录 5A）"></a>（4）字符与字符串（附录 5A）</h5><h5 id="（5）校验码：附录-5C，汉明码-4-2-6-课本-100-页-CRC-校验，上课补充"><a href="#（5）校验码：附录-5C，汉明码-4-2-6-课本-100-页-CRC-校验，上课补充" class="headerlink" title="（5）校验码：附录 5C，汉明码-4.2.6 课本 100 页 CRC 校验，上课补充"></a>（5）校验码：附录 5C，汉明码-4.2.6 课本 100 页 CRC 校验，上课补充</h5><h4 id="2-定点数的表示和运算"><a href="#2-定点数的表示和运算" class="headerlink" title="2. 定点数的表示和运算"></a>2. 定点数的表示和运算</h4><h5 id="（1）定点数的表示：无符号数、带符号数（6-1）"><a href="#（1）定点数的表示：无符号数、带符号数（6-1）" class="headerlink" title="（1）定点数的表示：无符号数、带符号数（6.1）"></a>（1）定点数的表示：无符号数、带符号数（6.1）</h5><h5 id="（2）定点数的运算：位移（参唐朔飞老师课本）、原码定点加减、补码定点加减、定点数乘除运算、溢出的概念和判别方法（6-3）"><a href="#（2）定点数的运算：位移（参唐朔飞老师课本）、原码定点加减、补码定点加减、定点数乘除运算、溢出的概念和判别方法（6-3）" class="headerlink" title="（2）定点数的运算：位移（参唐朔飞老师课本）、原码定点加减、补码定点加减、定点数乘除运算、溢出的概念和判别方法（6.3）"></a>（2）定点数的运算：位移（参唐朔飞老师课本）、原码定点加减、补码定点加减、定点数乘除运算、溢出的概念和判别方法（6.3）</h5><h4 id="3-浮点数的表示和运算"><a href="#3-浮点数的表示和运算" class="headerlink" title="3. 浮点数的表示和运算"></a>3. 浮点数的表示和运算</h4><h5 id="（1）浮点数的表示：IEEE754-标准。（6-2）"><a href="#（1）浮点数的表示：IEEE754-标准。（6-2）" class="headerlink" title="（1）浮点数的表示：IEEE754 标准。（6.2）"></a>（1）浮点数的表示：IEEE754 标准。（6.2）</h5><h5 id="（2）浮点数的加减运算（6-4）"><a href="#（2）浮点数的加减运算（6-4）" class="headerlink" title="（2）浮点数的加减运算（6.4）"></a>（2）浮点数的加减运算（6.4）</h5><h4 id="4-算术逻辑单元-ALU（6-5）"><a href="#4-算术逻辑单元-ALU（6-5）" class="headerlink" title="4. 算术逻辑单元 ALU（6.5）"></a>4. 算术逻辑单元 ALU（6.5）</h4><h5 id="（1）串行加法器和并行加法器"><a href="#（1）串行加法器和并行加法器" class="headerlink" title="（1）串行加法器和并行加法器"></a>（1）串行加法器和并行加法器</h5><h5 id="（2）算术逻辑单元-ALU-的功能和结构"><a href="#（2）算术逻辑单元-ALU-的功能和结构" class="headerlink" title="（2）算术逻辑单元 ALU 的功能和结构"></a>（2）算术逻辑单元 ALU 的功能和结构</h5><p><img src="https://img-blog.csdnimg.cn/20200304160932931.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzYyNzExOA==,size_16,color_FFFFFF,t_70" srcset="/img/loading.gif" lazyload alt="在这里插入图片描述"></p>
<h4 id="5-进制及其转换："><a href="#5-进制及其转换：" class="headerlink" title="5.进制及其转换："></a>5.进制及其转换：</h4><h5 id="2-8-10-16-进制及其互换"><a href="#2-8-10-16-进制及其互换" class="headerlink" title="2,8,10,16 进制及其互换"></a>2,8,10,16 进制及其互换</h5><h5 id="二进制和十进制的互换"><a href="#二进制和十进制的互换" class="headerlink" title="二进制和十进制的互换"></a>二进制和十进制的互换</h5><h6 id="①-纯整数"><a href="#①-纯整数" class="headerlink" title="① 纯整数"></a>① 纯整数</h6><h6 id="②-纯小数"><a href="#②-纯小数" class="headerlink" title="② 纯小数"></a>② 纯小数</h6><pre><code class="hljs">   0.5 0.1
   0.25 0.01
   0.125 0.001
</code></pre>
<h6 id="③-特殊分数：以-2-的幂次方为分母的分数"><a href="#③-特殊分数：以-2-的幂次方为分母的分数" class="headerlink" title="③ 特殊分数：以 2 的幂次方为分母的分数"></a>③ 特殊分数：以 2 的幂次方为分母的分数</h6><h6 id="二进制与八进制和十六进制的互换"><a href="#二进制与八进制和十六进制的互换" class="headerlink" title="二进制与八进制和十六进制的互换"></a>二进制与八进制和十六进制的互换</h6><pre><code class="hljs">   以小数点为起点
</code></pre>
<h4 id="6-真值和机器数的互换"><a href="#6-真值和机器数的互换" class="headerlink" title="6.真值和机器数的互换"></a>6.真值和机器数的互换</h4><h5 id="真值："><a href="#真值：" class="headerlink" title="真值："></a>真值：</h5><h5 id="机器数："><a href="#机器数：" class="headerlink" title="机器数："></a>机器数：</h5><figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><code class="hljs c"><span class="hljs-type">int</span> a;  <span class="hljs-comment">//申请了一个32内存空间，这个空间的地址叫a;</span><br>		<span class="hljs-comment">//也告诉了计算机把这个数当作有符号的数来看待，计算机会把它当作补码使用。</span><br>a=<span class="hljs-number">-5</span>;  <span class="hljs-comment">//计算机会存储 1011 即补码</span><br></code></pre></td></tr></table></figure>

<h5 id="原码，补码，反码，移码"><a href="#原码，补码，反码，移码" class="headerlink" title="原码，补码，反码，移码"></a>原码，补码，反码，移码</h5><h6 id="1-原码：符号位-绝对值的二进制-方便读取）"><a href="#1-原码：符号位-绝对值的二进制-方便读取）" class="headerlink" title="1.原码：符号位+绝对值的二进制(方便读取）"></a>1.原码：符号位+绝对值的二进制(方便读取）</h6><h6 id="2-补码：正数的补码等于原码-方便运算）"><a href="#2-补码：正数的补码等于原码-方便运算）" class="headerlink" title="2.补码：正数的补码等于原码(方便运算）"></a>2.补码：正数的补码等于原码(方便运算）</h6><pre><code class="hljs">           负数：除符号位外，各位取反末位加1
</code></pre>
<h6 id="3-反码：正数的反码等于原码（没用）"><a href="#3-反码：正数的反码等于原码（没用）" class="headerlink" title="3.反码：正数的反码等于原码（没用）"></a>3.反码：正数的反码等于原码（没用）</h6><pre><code class="hljs">           负数：除符号位外，各位取反
</code></pre>
<h6 id="4-移码：补码符号位取反"><a href="#4-移码：补码符号位取反" class="headerlink" title="4.移码：补码符号位取反"></a>4.移码：补码符号位取反</h6><h6 id="5-8421CD-码与余三码"><a href="#5-8421CD-码与余三码" class="headerlink" title="5.8421CD 码与余三码"></a>5.8421CD 码与余三码</h6><p><img src="https://img-blog.csdnimg.cn/20200304161333963.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzYyNzExOA==,size_16,color_FFFFFF,t_70" srcset="/img/loading.gif" lazyload alt="在这里插入图片描述"><br>8421BCD 用于表示字符型数据：电话号码、学号等，不用于运算<br><strong>大小比较：</strong><br>原码：正数越大值越大，负数越大值越小<br>移码：看着越大值越大<br>00000</p>
<h4 id="7-字符与字符串"><a href="#7-字符与字符串" class="headerlink" title="7.字符与字符串"></a>7.字符与字符串</h4><h5 id="输入码：音码（汉语拼音-和形码-五笔输入法）"><a href="#输入码：音码（汉语拼音-和形码-五笔输入法）" class="headerlink" title="输入码：音码（汉语拼音) 和形码 (五笔输入法）"></a>输入码：音码（汉语拼音) 和形码 (五笔输入法）</h5><h5 id="国标码："><a href="#国标码：" class="headerlink" title="国标码："></a>国标码：</h5><pre><code class="hljs">将汉字分为94行和94列
</code></pre>
<h5 id="机内码"><a href="#机内码" class="headerlink" title="机内码"></a>机内码</h5><h5 id="字体库"><a href="#字体库" class="headerlink" title="字体库"></a>字体库</h5><h4 id="8-校验码："><a href="#8-校验码：" class="headerlink" title="8.校验码："></a>8.校验码：</h4><h5 id="1）-双方约定："><a href="#1）-双方约定：" class="headerlink" title="(1） 双方约定："></a>(1） 双方约定：</h5><p>1.方法<br> 2.校验位的位数<br>3 校验位的位置</p>
<ol start="2">
<li>奇偶校验码：<br>. 优点：<br>简单<br>传输效率高 2. 缺点：<br>只能发现 Error<br>只能发现奇数个位数的错误</li>
<li>Hamming 码：<br>数据位 D（d 位）<br>校验位 R（r 位）</li>
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